Ontology and Geographic Kinds

Barry Smith[1] and David M. Mark[2]
National Center for Geographic Information and Analysis and
Center for Cognitive Science
University at Buffalo
Buffalo, New York, 14261 U.S.A.

Abstract

An ontology of geographic kinds is designed to yield a better understanding
of the structure of the geographic world, and to support the development of
geographic information systems that are conceptually sound. This paper
first demonstrates that geographical objects and kinds are not just larger
versions of the everyday objects and kinds previously studied in cognitive
science. Geographic objects are not merely located in space, as are the
manipulable objects of table-top space. Rather, they are tied intrinsically
to space, and this means that their spatial boundaries are in many cases
the most salient features for categorization. The ontology presented here
will accordingly be based on topology (the theory of boundary, contact and
separation) and on mereology (the theory of extended wholes and parts).
Geographic reality comprehends mesoscopic entities, many of which
are best
viewed as shadows cast onto the spatial plane by human reasoning and
language. Because of this, geographic categories are much more likely to
show cultural differences in category definitions than are the manipulable
objects of table-top space.

Keywords: ontology, mereology, geographic kinds, entity types, GIS

1
Introduction

Ontology deals with the nature of being. Communication requires a sharing
of
ontology between the communicating parties. The formal description of
ontology
is thus essential to data exchange standards, and to the design of
human-computer interfaces. In this paper, we describe some fundamentals of
the
ontology of geographic space and of the objects and phenomena of geographic
space.

1.1
Why Construct an Ontology?

An ontology of geographic kinds, of the categories or entity types in the
domain of geographic objects, is designed to yield a better understanding of
the structure of the geographic world. The results can be of practical
importance in at least the following ways:

First, understanding the ontology of geographic kinds can help us to
understand
how different groups of humans, for example different armies in a
multinational
coalition in time of war, exchange, or fail to exchange, geographic
information.

Second, understanding the ontology of geographic kinds can help us to
understand certain characteristic types of distortions that are involved in our
cognitive relations to geographic phenomena. Above all, there are tendencies
in
the conceptualization of geopolitical entities that underlie certain forms of
territorially based conflict.

Third, geographic information systems need to manipulate representations of
geographic entities, and ontological study of the corresponding entity types,
especially those at the basic level, will provide default characteristics for
such systems.

Fourth, entity types are a central issue in data exchange standards, where a
substantial part of the semantics of the data may be carried by the types that
instances are assigned to (Mark 1993). Research in ontology as a basis
for the development of knowledge-interchange standards has expanded
tremendously in recent years (Gruber 1993). This paper is designed as a
contribution to such research in the specific field of geography.

1.2
Specific Marks of Geographic Kinds

In what follows, we shall be interested in the theoretical peculiarities of
geographic kinds--in those features that set them apart from kinds of other
sorts. These features derive primarily from the fact that geographic objects
are not merely located in space, but are tied intrinsically to space in a
manner that implies that they inherit from space many of its structural
(mereological, topological, geometrical) properties.

Existing research on cognitive categories has standardly addressed entities on
the sub-geographic scale: manipulable entities of the table-top world,
objects of roughly human scale (birds, pets, toys) and other similar
phenomena. For such entities, the 'what' and the 'where' are almost always
independent. In the geographic world, in contrast, the 'what' and the 'where'
are intimately intertwined. In the geographic world, categorization is also
very often size- or scale-dependent. (Consider: pond, lake,
sea, ocean.) In the geographic world, to a much greater extent
than in the world of table-top space, the realization that a thing exists at
all may have individual or cultural variability. In the geographic world, too,
the boundaries of the objects with which we have to deal are themselves
salient
phenomena for purposes of categorization. These boundaries may be crisp or
graded, and they may be subject to dispute. Moreover, the identification of
what a thing is may influence the location and structure of the boundary; for
example, if a given topographic feature is identified as a marsh, then its
boundary may be located farther up the slope than would be the boundary of
the
same feature if it had been identified as a lake. These are all features of
categorization that are all but absent from the table-top world upon which
theories of categorization have hitherto been based.

1.3
Categories versus Sets

Science has typically modeled categories as sets in the mathematical sense,
and
the assumption of a set-theoretic model of categories is commonly made in
feature coding schemes, either explicitly (as in geocartographic data
standards) or implicitly. Every possible object or event is assumed to be
either a member or not a member of each particular set. This view of
categories
also assumes that there are procedures or rules available for determining set
membership from the observable characteristics of the individual.
Furthermore,
it is assumed that every member of a set would be an equally good exemplar
of
that set. This familiar model also underlies multivariate mathematical
models
of classes, such as those used in discriminant analysis, and in most forms of
cluster analysis.

The problems with the set-theoretic model as an account of the categories
used
by ordinary humans in everyday situations are clear. For most such
categories,
and for most people, some members are better examples of the class than are
others; furthermore, there is a great degree of agreement among human
subjects
as to what constitute good and bad examples. Rosch and others have
accordingly
proposed that natural kinds be seen as possessing a radial structure, having
prototypes of more central or typical members surrounded by a penumbra of
less
central or less typical instances (Rosch 1973, 1978). Following Couclelis
(1988), Mark (1989), and Mark and Frank (1996), a view along these lines will
be accepted in what follows.

1.4
Basic Tools of Ontology: Mereology and Topology

Geographic objects are spatial objects on or near the surface of the earth.
Furthermore, they are objects of a certain minimal scale (roughly: of a scale
such that they cannot be surveyed unaided within a single perceptual act).
Geographic objects are typically complex, and they will in every case have
parts. An adequate ontology of geographic objects must therefore contain a
theory of part and whole, or mereology (Simons 1987).

Geographic objects do not merely have constituent object-parts, they also
have
boundaries, which contribute as much to their ontological make-up as do the
constituents that they comprehend in their interiors. Geographic objects are
prototypically connected or contiguous, but they are sometimes
scattered
or separated. They are sometimes closed (e.g., lakes), and sometimes open
(e.g., bays). Note that the above concepts of contiguity and closure are
topological notions, and thus an adequate ontology of geographic objects must
contain also a topology, a theory of boundaries and interiors, of connectedness
and separation, that is integrated with a mereological theory of parts and
wholes (Smith 1996). The topological structure will bring with it certain sorts
of duality, thus for example dual to the distinction between the outer
boundary
and the interior of a geographic object is the distinction, within the
surrounding container or host, between the inner boundary of this
container and the exterior or hinterland beyond. Our topological
ontology
also must be able to cope with the fact that the very notion of 'boundary' can
mean, in different contexts, either an abstract mathematical
boundary--conceptualized as an infinitely thin line, plane or surface that is
located in space but does not occupy (fill out) space--or a boundary zone, of
small but finite thickness. Boundaries in the abstract sense are normally seen
as falling within the province of standard mathematical topology. For
geographical purposes, however, even within the category of abstract
boundaries
there are certain sorts of boundary phenomena which standard topology
cannot
deal with. If we cut an object--for instance a land parcel, or an island--in
half, we are not left with one piece that is closed and another that is not.
This is because abstract boundaries do not take up space, and thus they can be
perfectly co-located one with another. To do justice to such phenomena we
need
to use special mereotopological theories that depart in crucial ways from
standard topology (Smith and Varzi 1997).

An object is 'closed' in the mereotopological sense, if it includes its outer
boundary as part; it is 'open' if this outer boundary is included rather in its
complement. Ordinary material objects are in unproblematic fashion the
owners
of their surfaces. Where a complement meets an object of this sort, the object
will be closed and the complement open (Asher and Vieu 1995). Regarding
geographic objects, however, matters are not so simple. Consider the mouth
of a
volcano: where the hole meets its material host (the crater, a concave mass of
rock and debris), the boundary of the hole is the surface of the host. Thus the
boundary of the hole, there, belongs to the volcano, and not to the hole itself
(Casati and Varzi 1994). Consider, however, the boundary of the hole where it
is not in contact with its host: the boundary in the region corresponding to
the opening of the hole where it faces up towards the sky. Where do we place
the boundaries corresponding to those regions? Within the hole? Within the
sky?
Either choice would seem arbitrary, and a parallel situation is encountered in
the case of bays facing out towards the sea. This very arbitrariness will
reveal important features of geographic objects in general and of their
boundaries in particular.

2
Geographic Categories and the Geometry of Space

Geographic categories track not only mereology and topology but also
qualitative geometry (the theory of concavity, convexity, of shortness and
longness, the theory of being roughly round or roughly dumbbell shaped). A
theory of geographic categories must take account, too, of the fact that
geographic objects may be zero-, one-, two-, or three-dimensional. Consider
the North Pole, the Equator, Norway (a two-dimensional object with a
curvature
in three-dimensional space), or the North Sea. Consider also that 'North Sea'
may refer either to the three-dimensional body of water, or to its
two-dimensional surface. 'Bay' or 'sound' may refer to the surrounding land,
or
to the indentation in the shoreline, or to a part of the shoreline, as well as
the sheet or body of water. Note that there are different meanings of 'in'
(and of other spatial prepositions) according to what the relevant dimension
in
a given context might be: the island is 'in' the lake means, in one sense, that
it protrudes from the surface of the lake, in another sense that it is
completely submerged within the corresponding three-dimensional volume.

Ontologists since Aristotle have distinguished between two sorts of
predications: categorial predications as we are here using this term
(called by Aristotelians 'predications in the category of substance'): is a
man, is a fish, is a lake, etc.; and accidental predications (or
'predications in the category of accident'), for example: is red, is colored,
is big, is hungry. The former tell us under what category an object falls. They
tell us what an object is. The latter tell us how an object is, per
accidens, at a given moment; thus they pertain to ways in which
instances
of the relevant categories change from occasion to occasion.

There is no term for 'big dog' or 'small dog' corresponding to 'lake' and
'pond'. Why not? Because size for living objects is not usually a categorical
matter but is an attribute changes over time. In contrast, instances of
geographic categories characteristically do not grow or shrink (as animals do).
In this case, size and shape may be matters for categorical predication. The
question still remains whether lake is a basic level category in the
sense of Rosch (1978). Is pond a subordinate subclass, a-kind-of lake?
Or are lakes and ponds are both categories at the basic level, distinguished
mainly by size? Bay and cove, mountain and
hill,
form similar pairs. Empirical research with human subjects will be needed to
answer this and similar questions.

3
Levels of Reality

3.1
Spatial Reality

We use 'entity' and 'object' synonymously as ontological terms of art
comprehending things, relations, boundaries, events, processes, qualities,
quantities of all sorts. More specifically, in the context of geographic
ontology, 'object' and 'entity' shall comprehend regions, boundaries, parcels
of land, water-bodies, roads, buildings, bridges, and so on, as well as the
parts and aggregates of all of these.

We assume the existence of a real world, populated by real entities occupying
regions of space. Spatial regions form a relational system, comprising also
containment relations, separation relations, relations of adjacency and
overlap, and so on (Egenhofer and Herring 1991). We assume also the
existence
of a relation of being located at between things on the one hand (roads,
forests, wetlands), and the regions in or at which they are located on the
other (Casati and Varzi 1996).

3.2
The Cognitive Domain

On the other hand, there is the domain of cognition, of concepts, perception,
memory, reasoning and action. Counterparts of spatial relations exist in this
conceptual realm, too. Our cognitive acts are directed towards spatial objects
in the world. Interestingly, though, these acts themselves exist in a spatial
domain: they are tied to our bodies, which themselves exist in spatial reality,
so that some of our spatial concepts, like here or there, are
egocentric. Concepts therefore work spatially in manifold fashion: i) through
abstract models or representations of space in our minds, as when we think,
abstractly, about whether Peru is to the North or to the South of Ghana; ii)
through a concrete being-in-space, when we use indexical spatial concepts
such
as yonder, to the right, down east, etc.; and iii)
through
different sorts of mixtures of these. With geographic information systems
(GIS)
there is also iv): conceptual interaction with spatial entities that is
mediated through mathematical models and through computer
representations.

Matters are complicated further by the fact that our cognitive representations
of space may be under-defined or erroneous. They may show individual or
culture-related differences. They may be refined or modified through social
and
cultural interactions, formal education, and dictionary definitions. Some
spatial concepts may even be hard-wired into the perceptual systems in the
senses and brain. Other concepts may be changed through use; thus, once a
given
concept is judged to correspond with a particular situation, then the specifics
of that situation may modify the concept.

We assume that people think and reason by manipulating concepts; that
computer
programs are based on formal mathematical counterparts of relations
between
entities in the world; and that people use computers to learn about,
understand, or make decisions about such entities. Thus, establishing the
correspondences and interrelations among the different domains of spatial
entities and relations is essential to the construction of geographic
information systems and of other systems for reasoning about spatial entities
and relations.

3.3
Geographic Reality

Geographic reality has many different sorts of properties, features, entities
within it, which can be approached theoretically in many different ways.
There are aspects of spatial reality that have been well worked out by earth
scientists of various sorts. The cognitive aspects of this domain are however
still little understood from the theoretical point of view.
This is because those interested in cognition have, with few exceptions,
shown little interest in the spatial reality within which cognizing subjects are
situated, whereas those interested in spatial reality have shown for their part
little interest in cognition.
It is the interactions between these two
domains that are the principal object of our inquiries here. They relate to the
various ways in which human cognition and action, including social and
political action, lead to effects of an ontological sort within the domain of
spatial reality.

To fix our ideas, let us divide spatial reality into two sub-domains or strata,
which can be conceived, provisionally, as partitions of space at different levels
of granularity. (Conceive the two strata as laid on top of each other after the
fashion of map layers, with the upper stratum comprising objects of larger
scale.)

On the one hand is the microphysical stratum of spatial reality--it is
spatial reality as it is dealt with in the physical sciences. It may be
conceived, for present purposes, as a complex edifice of molecules. On the
other hand is the mesoscopic stratum of spatial reality. This is the
real-world counterpart of our non-scientific (naive, normal, everyday, lay)
cognition and action in space.

This mesoscopic stratum has three different types of components:

1. Objects of a straightforwardly physical sort--such as rivers, forests,
bridges--that are studied also by physics but which, as they are cognized
within the mesoscopic stratum, have different sorts of properties. (This is in
virtue of the fact that our naive cognition uses very little mathematics, has its
own peculiar topology, and endows its objects with qualitative rather than
quantitative features and with a social and cultural significance that is absent
from the microphysical realm.)

2. Geographic objects like bays and promontories, which are also in a sense
parts of the physical world but which exist only in virtue of demarcations
induced by human cognition and action.

3. Geopolitical objects like nations and neighborhoods which are more than
merely physical, and which exist only as the hybrid spatial products of human
cognition and action.

All three sets of components are spatial objects. Indeed we might conceive
mesoscopic entities in general as shadows cast by human reasoning and
language
(and by the associated activities) onto the spatial plane. All mesoscopic
objects exist as parts of spatial reality as we here conceive it. This applies
even to counties, land-parcels, postal districts, real estate subdivisions, air
corridors, and so on.

4
Problems with Geographical Extensions of Theories of Categorization Based
on
the Phenomena of Table-Top Space

The Rosch-style examples of small mammals, birds, utensils, etc., that have
been most extensively treated in the literature on categorization, differ from
geographic examples in a number of ways. First, they almost always involve
discrete, movable, items. And while research on categorization by cognitive
scientists does indeed indicate that humans tend quite generally to discretize
even where they are dealing with what are essentially continuous
phenomena (as
is shown, not least, by the case of GIS), an adequate ontology of geographic
kinds should embrace not only categories of discreta but also categories that
arise in the realm of continuous phenomena.

Table-top examples tend further to reinforce a view according to which
nature
can be cut at its joints--that is, a view to the effect that there is a true,
God-given structure, which science attempts to make precise. As we shall see,
geographic categorization involves a degree of human-contributed
arbitrariness
on a number of different levels, and it is in general marked by differences in
the ways different languages and cultures structure or slice their worlds. It
is precisely because many geographical kinds result from a more-or-less
arbitrary drawing of boundaries in a continuum that the category boundaries
will likely differ from culture to culture (in ways that can lead to sometimes
bloody conflict as between one group or culture and another).

Finally, the familiar Rosch-style examples form a family of separate categorial
systems possessing simple tree structures, with each tree having little to do
with the other trees. Geographic categories, in contrast, because they relate
to objects intrinsically interrelated together within a single domain (called
space), form categorial systems that interact to form a single
structure. The mereological, topological and geometrical, organization of
space
thus has deep implications for the structure of our cognitive system of
geographic categories.

5
The Realm of Fiats

As shown above, geographic objects will often be identified by specification of
the locations of their boundaries. It is important to distinguish between
bona fide and fiat boundaries. Following Smith (1995), the
former are boundaries that correspond to genuine discontinuities in the
world,
the latter are projected onto geographic space in ways that are to a degree
independent of such discontinuities. The surfaces of extended objects such as
planets or tennis balls are clearly boundaries of the bona fide sort. Shorelines
and water courses can also readily be considered to be bona fide boundaries.
In contrast, many state and provincial borders, as well as county lines and
property lines and the borders of postal districts, provide examples of
boundaries of the fiat sort, especially in those cases where, as in the case of
Colorado or Alberta, they lie skew to any pre-existing qualitative
differentiations or spatial discontinuities (coastlines, rivers) in the underlying
territory. Boundaries of areas of a given soil type, of wetlands, or of bays or
mountains are also at least partly of the fiat type, although here the
boundaries may result from cognitive rather than from legal or political
processes.

Once fiat outer boundaries have been recognized, it becomes clear that the
opposition between bona fide and fiat boundaries can be drawn not merely in
relation to boundaries but in relation also to the objects that they bound.
Examples of bona fide geographic objects are the planet Earth, Vancouver
Island, the Dead Sea. Fiat objects include King County, the State of Wyoming,
the Tropic of Cancer. There are, of course, cases of objects that ought
reasonably to be classified as fiat objects whose boundaries involve a mixture
of bona fide and fiat elements. Haiti and the Dominican Republic, which
together occupy the Island of Hispaniola, are examples which spring to mind,
but every national boundary will in course of time involve boundary-
markers:
border-posts, watch-towers, barbed wire fences and the like, which lend a
physical aspect to what was initially an object of the fiat sort.

5.1
Types of fiat boundary

There are various different ways in which we can divide up the realm of fiat
boundaries: some fiat boundaries are long-standing, crisp and determinate,
the
products of deliberate legislation; others are vague or transient, the products
of momentary territorial adjustments (for example in battle zones). Fiat
boundaries all have in common that they exist only in virtue of the different
sorts of demarcations effected cognitively and behaviorally by human beings.
But they are
otherwise of many sorts. They may be complete or incomplete, symmetrical
or
asymmetrical. They may lie entirely skew to all boundaries of the bona fide
sort, may involve a combination of fiat and bona fide portions, or they may be
constructed entirely out of bona fide portions that however, because they are
not themselves intrinsically connected, must be glued together in fiat fashion
in order to yield a boundary that is topologically complete. We will deal with
this manifold variety of fiat boundaries in some detail in what follows.

5.2
Fiats and vagueness

There are fiat objects (deserts, valleys, etc.) that are delineated not by
crisp outer boundaries but rather by boundary-like regions that are to some
degree indeterminate. This is not to say that the ontology we are here
expounding is ultimately vague--that the fundamental categorial scheme
should
allow for a distinction between crisp and scruffy (fuzzy, hazy, indeterminate)
entities, as some have urged. Rather, vagueness is a conceptual matter: if you
point to an irregularly shaped protuberance in the sand and say 'dune', then
the correlate of your expression is a fiat object whose constituent unitary
parts are comprehended (articulated) through the concept dune. The
vagueness of
the concept itself is responsible for the vagueness with which the referent of
your expression is picked out. Each one of a large variety of slightly
different and precisely determinate aggregates of molecules has an equal
claim
to being such a referent. When you have a map, and it has a shoreline with
ins
and outs, and on the water adjacent to one of the ins is a label saying 'Baie
d'Ecaigrain', it is fairly easy for a human to see where the bay is. The outer
boundary of the bay (seaward) is probably irrelevant to action or practice,
unless some regulators have ceded all the islands (or oil) in the bay to some
other country. But try to tell a computer that the bay is here, and that it
extends from there to there on the coastline, but then just fades off to
seaward, and get the computer to reason with that information the way that a
person would.

Mountains, hills, ridges, also a cape or point--we can all agree that they are
real, and that it is obvious where the top of a mountain or the end of a cape
is to be found. But where is the boundary of Cape Flattery on the inland side?
Where is the boundary of Mont Blanc among its foothills?

5.3
Consensus Fiats

Fiat boundaries may be products of informal consensus, reflecting for
example
linguistic usage as this evolves informally over time. Bays, peninsulas, etc.,
are parts of spatial reality, physical parts of the world itself. But they are
parts of reality that would not be there absent corresponding linguistic and
cultural practices of demarcation and categorization.

In a world with our everyday human practices, a bay or a hill is just as real
as a chair or rock. The former are real consensus fiat objects, the latter are
real bona fide objects. Bona fide objects are for obvious reasons more likely
to be objects of categorizations that enjoy a high degree of cross-cultural
invariance. Fiat objects, in contrast, because they are inculcated into the
world by cognition, are more likely to show cultural dependence.

5.4
Legal fiats

Some fiat boundaries, like the boundaries of nations or postal districts, are
social entities, analogous to rights, claims and obligations. Usually, when the
legal system takes a fuzzily bounded region, it has to add a rule to crisp up
the boundary. Private property in some jurisdictions extends to the mean low
water mark, and for any seacoast part of the US or Canada you would find a
legal definition based on mean low, high, average, etc. tide level, as to where
private property stops and a commons starts. The boundary between the
North
West Territories and the provinces of Manitoba, Ontario, and Quebec around
Hudson and James Bays in Canada, is the mean low tide level. And then
there is
a definition of how the boundary crosses the mouths of rivers. A
legally-protected wetland has to have standing water on average more than n
days per year. There may also be a minimum size rule. There is an area in
Jim's
back yard about 3 x 5 meters, that might qualify as a federal wetland, but
might not be detectable by the appropriate authorities.

If one needs to know where the shoreline is, perhaps in order to regulate
access or trespassing, then one selects some particular stage in the tidal
cycle, such as mean low tide level; this produces a fiat shoreline that is
fixed and reasonably crisp, and that approximates a bona fide shoreline that
moves with the waves and tides. You cannot see or touch or trip over the fiat
shoreline; but the fiat shoreline is there, nonetheless, as a part of reality:
if you cross it, you may be prosecuted.

5.5
GIS fiats

Fiat crisping occurs also in the scientific realm. Consider soil, a
continuously-varying mass of material that lies, in most places, just below the
surface of the earth. At a scale of sand grains and roots, it might be thought
of as made up of a myriad of objects or entities. But at a larger scale, the
percentage of sand, silt, and clay often varies gradually and continuously over
space, as might water content, pH, organic content, thickness, etc. Soil
scientists have traditionally imposed upon this continuum a set of nominal
soil
types (categories or kinds); these are mathematical fiats that are artifacts of
a certain technology. They might, for example, be some function of
measurable
quantities of a sample of the soil. If pH < 7.3 and percentage sand < 10
and percentage organic < 2, and thickness < 1.1 m, then it is type X.
Soil chemical and physical properties may constitute fields that vary more or
less
continuously and somewhat independently across geographic space. In such
a
system, soil boundaries are pieces of the 7.3 pH isoline, the 1.1 meter
isopach, and so on. With perfect information, we can apply that typology to
the
continuous variables and get crisp boundaries for soil types. We can then
represent the patch of soil of that type as a polygon, or draw the boundary
with ink, and see soil as a world of geographic objects with crisp boundaries.
These are scientific fiat boundaries, not bona fide boundaries. If we change
the classification system, our boundaries will move; some of them will
disappear; new ones will have to be created. If we do not keep the original
continuous data, we cannot even determine where the new boundaries
should be.

Soil scientists in the field of course do not measure everywhere. They observe
where the boundaries probably are, and draw them on the map, based on
changes
in underlying geology, in vegetation, in topography. Then they dig in the
middle of each polygon, and use the results obtained in the laboratory to
classify the whole polygon. It is said that soil scientists seldom sample near
the boundaries, perhaps because they know that they are not really there.
Fields for each soil property would be a better thing to store. The polygons
with crisp boundaries misrepresent the phenomenon, but they were the best
that
could be done with static, printed, ink-on-paper media.

5.6
Fiats in the realm of concepts

The concept of fiat boundary was introduced as a means of doing justice to the
fact that we divide up the spatial reality out there in more or less arbitrary
fashion into sub-regions. But there is an element of arbitrariness or fiat also
in the domain of our concepts themselves: we can partition the family of
spatial concepts, of geographic entity-types, in more or less arbitrary ways
into sub-concepts.

Imagine the instances of a concept arranged in a quasi-spatial way, as happens
for example in familiar accounts of color- or tone-space. Suppose that each
concept is associated with some extended region in which its instances are
contained, and suppose further that this is done in such a fashion that the
prototypes, the most typical instances, are located in the center of the
relevant region, and the less typical instances are located at distances from
this center in proportion to their degree of non-typicality. Boundary or fringe
cases can now be defined as those cases that are so untypical that even the
slightest further deviation from the norm would imply that they are no
longer
instances of the given concept at all.

In this fashion counterparts of the familiar topological notions of boundary,
interior, contact, separation, and continuity can be defined for the conceptual
realm, and the notion of similarity as a relation between instances can be
understood as a topological notion (Mostowski 1983; Petitot, 1994). In the
realm of colors,
for example, a is similar to b might be taken to mean that the colors of a and
b lie so close together in color-space that they cannot be discriminated with
the naked eye. A similarity relation is in general symmetric and reflexive, but
it falls short of transitivity, and is thus not an equivalence relation. This
means that it partitions the space of instances not into tidily disjoint and
exhaustive equivalence classes, but rather into overlapping circles of
similars. This falling short of the discreteness and exhaustiveness of
partitions of the type that are generated by equivalence relations is
characteristic of topological structures. In some cases, there is a continuous
transition from one concept to its neighbors in concept-space, as for example
in the transition from lake to marsh to wetland. In other cases, circles of
similars are separated by gaps (regions of concept-space that have no
instances). This is so regarding the transition from, say, lake to reservoir.

Terms like 'strait' and 'river' represent arbitrary partitions of the world of
water bodies. The English language might have evolved with just one term,
or
three terms, comprehending the range of phenomena stretching between
strait and river or, in French, between détroit
and
fleuve. For while the Straits of Gibraltar are certainly not a river,
and the Mississippi River is certainly not a strait, there are cases--such as
the Detroit River and the Bosporus--that exist on the borderline between the
categories. All are flat, narrow passages that ships can sail through between
two larger water bodies (lakes, seas), and all have net flow through them, due
to runoff, etc. Is Lake Erie really a lake, or just a wide, deep part of the
river-with-five-names that is called the St. Lawrence as it flows into the sea?
Well, that depends on what you mean by 'lake'.

6
Conclusions and Future Work

In this paper, we have presented some reasons why ontologies for geographic
objects will differ from the ontologies of everyday objects commonly
examined
by philosophers and cognitive scientists. For one thing, topology and
part-whole relations appear to be much more important in the geographic
domain.
Research on this topic must be careful to distinguish the domain of the real
world from the domain of computational and mathematical representations,
and
both of these from the cognitive domain of reasoning, language, and human
action. Human practice is an important part of the total ontology. Cultural
differences in categorizations are more likely to be found for geographic
entities than for objects at table-top scales. Geographic ontologies are more
strongly focused on boundaries, and a typology of boundaries is critical. Work
involving formal comparisons of geospatial and cartographic data standards
and
dictionary definitions in a variety of languages will provide an important
starting point for the cross-cultural experiments with human subjects that
will
be needed to refine the details of the ultimate ontology of geographic kinds.

7
Acknowledgements

This paper is a part of Research Initiative
#21, "Formal Models of Common-Sense Geographic Worlds", of the National
Center
for Geographic Information and Analysis, supported by grants from the
National
Science Foundation (SBR-8810917 and SBR-9600465); support by NSF is
gratefully
acknowledged.

8
References

Asher, N., and Vieu, L., 1995. Toward a Geometry of Common Sense: A
Semantics
and a Complete Axiomatization of Mereotopology, Proceedings of the 14th
International Joint Conference on Artificial Intelligence, San Mateo, CA:
Morgan Kaufmann, pp. 846-52.